How many roots does the equation || x +2 | - 2 | = 2 have?
A. 0
B. 1
C. 2
D. 3
E. 4
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Pls help 2 :How many roots does this equation have?
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Case 1: |x+2| - 2 = 2, implying that |x+2| = 4himu wrote:How many roots does the equation || x +2 | - 2 | = 2 have?
A. 0
B. 1
C. 2
D. 3
E. 4
If x+2 = 4, then x=2.
If x+2 = -4, then x=-6.
For Case 1, there are two solutions: x=2 and x=-6.
Case 2: |x+2| - 2 = -2, implying that |x+2| = 0
For Case 2, there is only one solution: x=-2.
Total solutions:
x=-6, x=-2, x=2.
The correct answer is D.
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Hi himu,
Since this equation has an absolute value embedded inside another absolute value, the key to solving it is to work from the "outside" in...
We're given || X +2 | - 2 | = 2
Let's rewrite this as...
||something| - 2| = 2
Taking the "-2" and the "outside" absolute value into account, we need the left "side" of the calculation to equal EITHER 2 or -2....
So....
|something| - 2 = 2
|something| - 2 = -2
In the first option, we need |something| to equal 4
In the second option, we need |something| to equal 0
Now we can deal with the inner absolute value....
|X + 2| = 4
This has two solutions: -6 and +2
|X + 2| = 0
This has one solution: -2
Thus, we have 3 solutions/roots.
Final Answer: D
GMAT assassins aren't born, they're made,
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Since this equation has an absolute value embedded inside another absolute value, the key to solving it is to work from the "outside" in...
We're given || X +2 | - 2 | = 2
Let's rewrite this as...
||something| - 2| = 2
Taking the "-2" and the "outside" absolute value into account, we need the left "side" of the calculation to equal EITHER 2 or -2....
So....
|something| - 2 = 2
|something| - 2 = -2
In the first option, we need |something| to equal 4
In the second option, we need |something| to equal 0
Now we can deal with the inner absolute value....
|X + 2| = 4
This has two solutions: -6 and +2
|X + 2| = 0
This has one solution: -2
Thus, we have 3 solutions/roots.
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
